Double Gamow-Teller Research Articles

Correlation between neutrinoless double-β decay and double Gamow-Teller transitions

The neutrinoless double-β (0νββ) decay and the double Gamow-Teller (DGT) transition are investigated with the state-of-the-art Relativistic Configuration-interaction Density functional theory. A strong linear correlation between the nuclear matrix elements (NMEs) of the 0νββ decay and the DGT transition is demonstrated. This linear correlation is found to originate from the similarity of the leading-order term of the 0νββ-decay operator and the DGT-transition one, as revealed by expanding the 0νββ-decay operator in terms of the spherical harmonics. The present results provide a strong support to constrain the 0νββ-decay NMEs through the double charge-exchange reactions.

Correlations between neutrinoless double- β , double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework

We explore the relation between the nuclear matrix elements of neutrinoless double-beta ($0\nu\beta\beta$) decay and two other processes: double Gamow-Teller (DGT) and double-magnetic dipole (M1M1) transitions, with focus on medium-mass to heavy nuclei studied with the proton-neutron quasiparticle random-phase approximation (pnQRPA) framework. We explore a wide span of isoscalar proton-neutron pairing strengths covering the typical range of values that describe well $\beta$- and two-neutrino $\beta\beta$-decay data. Our results indicate good linear correlations between $0\nu\beta\beta$ and both DGT and M1M1 matrix elements. Together with future measurements of DGT and M1M1 transitions, these correlations could help constrain the values of the $0\nu\beta\beta$-decay nuclear matrix elements.

Double charge exchange reactions as a probe for neutrinoless double beta decay nuclear matrix elements

The formalism to describe heavy-ion double charge exchange (DCE) processes in the eikonal and small-momentum transfer approximations introduced in Phys. Rev. C 98, 061601(R) (2018) is briefly discussed. It is also shown that, under the previous approximations, the heavy-ion DCE cross-section can be factorized in terms of a reaction and a nuclear part. A double charge exchange effective potential is explicitly derived in the closure approximation and also for the first time the explicit form of the DCE nuclear matrix elements, that are of the form of double Gamow-Teller and double Fermi. The recent hypothesis of a linear correlation between double Gamow-Teller neutrinoless double beta decay and DCE nuclear matrix elements is confirmed thanks to the first explicit derivation of DCE nuclear matrix elements, and by means of microscopic IBM2 calculations.

Double charge-exchange phonon states

We study double charge-exchange phonon states in neutron-rich nuclei, in particular the double isobaric analog states and the double Gamow-Teller excitations, induced by the double isospin operator $\sum_{i,j=1}^At_-(i) t_-(j)$ and spin-isospin operator $\sum_{i,j=1}^A{\sigma}(i) t_-(i){\sigma}(j) t_-(j)$, respectively. We employ quartic commutator relations to evaluate the average energies $E_{\rm DIAS} - 2E_{\rm IAS}$ and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})$, and conventional double commutator relations to evaluate the average energies of $E_{\rm GTR}-E_{\rm IAS}$ and $E_{\rm IAS}$. We have found that the corrections due to quartic commutators follow the approximate laws: $E_{\rm DIAS} - 2E_{\rm IAS}\approx \frac{3}{2} A^{-1/3}$ MeV and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})\approx 16 A^{-1}$ MeV. While the former is dominated by direct Coulomb effects, since Coulomb exchange cancels out to some extent with isospin symmetry breaking contributions originated form the nuclear strong force, the latter is sensitive to the difference in strength between the spin and spin-isospin chanels of the strong interaction.

Single and Double Charge Exchange Excitations of Spin-Isospin Mode

We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator (σt­)2 In general, 2+states in the granddaughter nuclei have dominant transition strength in DGT excitations and 0+states are weak, except in T = 1 mother nuclei in which 0+strength is competitive with 2+strength. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the (#x03C3;t­)2 excitation of double isobaric analog state (DIAS) in T = 1 nuclei.

Heavy-ion double-charge-exchange and its relation to neutrinoless double- β decay

We introduce the formalism to describe heavy-ion Double-Charge-Exchange (DCE) processes in the eikonal approximation. We focus on the low-momentum-transfer limit -- corresponding to the differential cross section at $\theta=0^\circ$ -- and, for the first time, we show that it is possible to factorize the DCE cross-section in terms of reaction and nuclear parts. Whereas in the $\theta\neq0^\circ$ case the nuclear part is a convolution of the beam and target nuclear matrix elements (NMEs), for $\theta=0^\circ$ we demonstrate - for the first time- that the transition matrix elements can be written as the sum of Double-Gamow-Teller (DGT) and Double Fermi (DF) type parts, and that they can both be further factorized in terms of target and projectile NMEs. By making use of the Interacting Boson Model (IBM) formalism, we also show that the DGT and total parts of the neutrinoless double-beta decay NMEs are in linear correlation with DCE-DGT NMEs. This confirms the hypothesis of a linear correlation between them, as introduced in [Phys.\ Rev.\ Lett.\ {\bf 120}, 142502 (2018)]. The possibility of a Two-Step Factorization (TSF) of the very forward differential DCE-cross-section and the emergence of DGT and DF types for the DCE nuclear matrix elements, combined with a linear correlation between DCE-DGT and 0$\nu\beta\beta$ NMEs, opens the possibility of placing an upper limit on neutrinoless double-beta decay NMEs in terms of the DCE experimental data at $\theta=0^\circ$.

Nuclear structure studies of double-charge-exchange Gamow-Teller strength

The double Gamow-Teller strength distributions in even-$A$ Calcium isotopes were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of the parent nucleus. The number of intermediate states actually contributing to the results was determined. The sum rules for the double Gamow-Teller operator in the full calculation were approximately fulfilled. In the case that the symmetry is restored approximately by introducing degeneracies of the $f$-levels, and the $p$-levels in the $fp$-model space, the agreement with the sum rules was very close.

Is it possible to study neutrinoless ββ decay by measuring double Gamow-Teller transitions?

Searches of neutrinoless double-beta decay require information on the value of the nuclear matrix elements that rule the process to plan and interpret experiments. At present, however, even the matrix elements obtained with the most reliable many-body approaches do not agree to each other better than a factor two or three. A usual test of the many-body calculations is the comparison to several nuclear observables, but so far no nuclear structure property has been found to show a good correlation to neutrinoless double-beta decay. Here we propose that double charge-exchange experiments can offer a very valuable tool to provide insights on neutrinoless double-beta decay. Double charge-exchange reactions are being currently performed in various laboratories worldwide and aim to find the novel nuclear collectivity given by double Gamow-Teller excitations. Our results suggest a good linear correlation between double Gamow- Teller transitions to the ground state of the final nucleus and neutrinoless double-beta decay nuclear matrix elements. The correlation seems robust across pf-shell nuclei.

Double Gamow-Teller Transitions and its Relation to Neutrinoless ββ Decay.

We study the double Gamow-Teller (DGT) strength distribution of ^{48}Ca with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless ββ (0νββ) decay. We find a simple relation between the centroid energy of the ^{48}Ca DGT giant resonance and the 0νββ decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the 0νββ decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several ββ emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of 0νββ decay nuclear matrix elements.

Study of the double Gamow-Teller transitions using the shell model approach

The double Gamow-Teller strength distributions in the lightest double beta-decay candidate 48Ca and its isotope 46Ca were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of parent nucleus. The nuclear matrix element of the double Gamow- Teller transition from the ground state to the ground state that goes into the double beta decay calculation was shown as a small fraction of the total transition.

Sum rule study for double Gamow-Teller states

We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator $(\sigma t_-)^2$. In general, $2^+$ states in the granddaughter nuclei have dominant transition strength in DGT excitations and $0^+$ states are weak, except in $T=1$ mother nuclei in which $0^+$ strength is competitive with 2$^+$ strength. The isospin selection of DGT is also discussed among 5 possible isospin states in granddaughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the $(\sigma t_-)^2$ excitation of double isobaric analog state (DIAS) in $T=1$ nuclei.

Study of two neutrino β+β+/β+ EC/ECEC decay of 124, 126Xe and 130, 132Ba for 0+→ 0+ transition in PHFB model

We have calculated the double Gamow–Teller (DGT) matrix element M2νGT and half-life T2ν1/2 for two neutrino double beta decay (β+β+/β+EC/ECEC) of 124,126Xe and 130,132Ba in the Hartree–Fock–Bogoliubov framework. The reliability of the intrinsic wavefunctions of 124,126,130,132Xe, 124,126Te and 130,132Ba nuclei has been tested by comparing the theoretically calculated spectroscopic properties with the available experimental data. The calculated half-lives for the 0+→ 0+ transition range from 1022 years to 1029 years, varying from mode to mode indicating that β+ EC may be the process with the most potential to be detected using present experimental setups. Moreover, it can be inferred from the present study that deformation plays an important role in the quenching of M2νGT and hence is very crucial to be considered in the framework used to study double beta decay.

Deformation effect on the double Gamow-Teller matrix element of100Mofor the0+→0+transition

The two neutrino double beta decay of ${}^{100}\mathrm{Mo}$ for the ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ transition is studied in the Hartree-Fock-Bogoliubov (HFB) framework. Prior to the calculation of the double Gamow-Teller matrix element ${M}_{\mathrm{GT}}^{2\ensuremath{\nu}},$ the reliability of the intrinsic wave functions has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties and the available experimental data for ${}^{100}\mathrm{Mo}$ and ${}^{100}\mathrm{Ru}.$ It has been further noticed that there is a necessity of an appropriate amount of deformation in the HFB intrinsic state to obtain a realistic ${M}_{\mathrm{GT}}^{2\ensuremath{\nu}}.$

Sum-rule analysis of the renormalized quasiparticle random-phase approximation

The renormalized quasiparticle random-phase approximation (RQRPA) is analyzed by the use of sum-rule techniques in realistic model calculations. It is found that the RQRPA does not satisfy the Gamow-TellerS − −S +=3(N − Z) sum rule and that the violation mostly comes from theS − part of it. The violation also seems to be mass-dependent increasing towards lighter masses. At the same time also the double Gamow-Teller sum rule is seen to be violated. Possible restoration of the sum rule is seen in the inclusion of the scattering terms in the definition of the RQRPA phonon operators.

Systematic study of beta and double beta decay to excited final states

A systematic study of the two-neutrino double beta (2νββ) decay to the final ground state and excited states is performed within an extension of the quasiparticle random-phase approximation (QRPA) model. In this extension, the multiple commutator model (MCM), a simultaneous treatment of the double-odd and double-even nuclei is possible by assuming their states to have the structure of one or two QRPA phonons. The MCM calculation is done for nine 2νβ−β− decays and six 2νECEC decays, and systematics of the relevant matrix elements and half-lives have been created. The study of the 2νββ-decay rates is complemented with the MCM study of the single-beta-decay properties of the relevant nuclei within the double-beta isobaric chains. The Woods-Saxon single-particle energies have been corrected near the Fermi surface by comparing the BCS quasiparticle energies with spectroscopic data of odd-mass nuclei. Pairing gaps, energy systematics of the Gamow-Teller states and the available beta-decay data have been used to obtain effective, model-space adapted, two-body matrix elements starting from the G-matrix elements of the Bonn one-boson-exchange potential. This enables a parameter-free calculation of the double Gamow-Teller matrix elements and theoretical prediction of double-beta half-lives.

Search for double Gamow-Teller strength by heavy-ion double charge exchange

We have carried out a search for double Gamow-Teller excitations, employing the 24Mg( 18O, 18Ne) 24Ne reaction at 100 and 76 MeV/nucleon at NSCL-MSU and GANIL, respectively. The cross sections for low-lying excitations are typically a few nb/sr, providing evidence for a strong suppression of double Gamow-Teller excitations in heavy-ion double charge exchange, compared to pion-induced reactions. This result does not give good hope that heavy ions at intermediate energies could be used to probe double Gamow-Teller strength.

Sum rules for double Gamow - Teller excitation

Abstract Sum rules are presented for the double Gamow-Teller excitation with ΔT z =±2. The sum rules consist of a model-independent term which is expressed by the numbers of protons and neutrons, and model-dependent terms. It is demonstrated by a numerical calculation that the model-independent term represents a good estimate of the double Gamow-Teller strength for nuclei with N ⩾ Z +4. The calculation indicates that the strength is concentrated in lowest-isospin states, and a giant resonance is constructed near the double isobaric analog state. The double Gamow-Teller excitation favors an angular-momentum transfer of J = 2 rather than J = 0.

Nuclear structure studies of double Gamow-Teller and double beta decay strength

The double Gamow-Teller strength distribution is evaluated microscopically in a series of light and medium mass nuclei using the shell model approach. The specific 2β decay transition from the ground state to ground state is computed in all the nuclei considered and the model dependence of the result is studied. The importance of the coherence when summing over the intermediate states is studied and is found to be a crucial factor in most of the double Gamow-Teller transitions. The effects of SU(4) symmetry breaking are studied using several models and types of interactions. This breaking is much larger in medium mass nuclei ( A = 44) than in the lighter nuclei ( A = 8, 12, or 20). The behaviour of double Gamow-Teller ground state to ground state transition amplitudes on the size of the model space is found to be complicated and to be different for different nuclei. The probabilities of studying double Gamow-Teller strength in combined ( p, n) and ( n, p) experiment, in pion double charge-exchange, and charge-exchange reactions are discussed.

Nuclear structure studies of double Gamow-Teller and double beta decay strength: Dao-Chen Zheng and Larry Zamick. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855; Naftali Auerbach. School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

Nuclear structure studies of double Gamow-Teller and double beta decay strength: Dao-Chen Zheng and Larry Zamick. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855; Naftali Auerbach. School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

Generalization of the sum rule for double Gamow-Teller operators.

We show that for Pauli-blocked nuclei, in the closure approximation, the summed strength for the double Gamow-Teller ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ transitions is less than the value 6(N-Z)(N-Z+1) and that the difference can be related to sum rules for magnetic dipole transitions, which in turn can be related to the double Gamow-Teller matrix element for the transition from the ${0}^{+}$ initial state to its double isobaric analog state. A ``wrong isospin phase sum rule'' is found that is valid in limited cases.